{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-superlinearly-convergent-subgradient-method","title":"A superlinearly convergent subgradient method for sharp semismooth problems","arxiv_id":"2201.04611","date":"2022-01-12","proceeding":null,"authors":["Vasileios Charisopoulos","Damek Davis"],"abstract":"Subgradient methods comprise a fundamental class of nonsmooth optimization algorithms. Classical results show that certain subgradient methods converge sublinearly for general Lipschitz convex functions and converge linearly for convex functions that grow sharply away from solutions. Recent work has moreover extended these results to certain nonconvex problems. In this work we seek to improve the complexity of these algorithms, asking: is it possible to design a superlinearly convergent subgradient method? We provide a positive answer to this question for a broad class of sharp semismooth functions.","url_abs":"https://arxiv.org/abs/2201.04611v1","url_pdf":"https://arxiv.org/pdf/2201.04611v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-superlinearly-convergent-subgradient-method","repo_url":"https://github.com/cor-opt/superpolyak.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}